spatial econometric analysis of regional income convergence ...analysis (bea). the specific data set...

Research in Business and Economics Journal

Spatial econometric analysis, page 1

Spatial econometric analysis of regional income convergence:

The case of North Carolina and Virginia

Zachary Smith

Saint Leo University

Alan Harper

South University

ABSTRACT

The purpose of this study is to determine if and to what extent the states of North

Carolina and Virginia display regional income convergence. This study utilizes growth theory as

the theoretical foundation to explore this phenomenon. This paper uses OLS (ordinary least

squares) as the proposed methodology. The researchers seek to answer the following research

questions in this study: (a) Using a county-level of analysis, do the counties of Virginia and

North Carolina exhibit regional income convergence? (b) Using a county-level of analysis, do

the counties of Virginia and North Carolina exhibit regional sigma convergence? (c) Are there

any significant changes in the structure of both of these metrics of convergence over time? (d) Is

there evidence of spatial dependence in the county level growth rates in Virginia and North

Carolina? (e) Does the additional of the spatial lag of growth rates improve the models of

regional income convergence in our two states? Our results indicate that income convergence

and spatial dependence found in the North Carolinian counties is more pronounced than those

experienced in the Virginian Counties.

Keywords: Virginia, North Carolina, Per Capita Income, Convergence, County-Level Analysis,

Spatial Lag Model

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INTRODUCTION

Income growth and convergence also known as the catch-up effect has been studied

extensively in the literature with most studies citing the works of Salow (1956). The benefits

associated with the catch-up effect have been well documented in the literature when viewed

through the lens of income convergence. The neo-classical premise behind this catch up effect is

associated with the constructs of beta and sigma convergence. Beta convergence simply means

that poorer regions will grow faster than richer regions holding all things equal, while sigma

convergence is related to a reduction in the disparity of incomes across economies. Despite the

many benefits associated with income convergence, there exists an apparent heterogeneity in the

literature with some research supporting income convergence (Baumol, 1986; Barro and Sala-i-

Martin, 1992), while other research supports income divergence (Mankiw, Romer and Weil,

1992). This study adds to this apparent heterogeneity in the literature.

Studies such as Rey, S. and Montouri, B. (1999), Clinch, J. and O’Neill, E. (2009),

Dall’erba, S. and Gallo, J. (2008), and Ertur, C. and Koch, W. (2007) have applied the spatial

econometric techniques to explore the dynamic process of regional income convergence to

attempt to advance our understanding of the convergence process. The aforementioned papers

explore spillover effects, technological diffusion, resource endowments, labor migration, poverty

traps, and labor market rigidities in an attempt to explain from a theoretical (i.e. model building)

and from a empirical perspective (i.e. examinations of regional spatial relationships) how these

spatial relationships influence the convergence process. In addition to adding to the

heterogeneity in the literature, in terms of beta and sigma convergence, this paper investigates

whether there is evidence of spatial dependence of regional income convergence occurring at a

county level of analysis in two neighboring states.

Studies of beta and sigma convergence as well as examinations of spatial dependence

typically make generalizations about the underlying individual units of observations and their

behavior over the period of investigation. This paper purports to explore the patterns embedded

in the beta convergence, sigma convergence, and spatial dependence statistics in an attempt to

better understand the dynamic behavior of regional income convergence. It is assumed that by

examining trends and patterns over time, researchers will uncover some meaningful implications

of the convergence process.

This purpose of this study is to determine if and to what extent North Carolinian and

Virginian counties display regional income convergence. This paper seeks to answer the

following research questions: (a) Using a county-level of analysis, do the counties of Virginia

and North Carolina Counties exhibit regional income convergence? (b) Using a county-level of

analysis, do the counties of Virginia and North Carolina exhibit regional sigma convergence? (c)

Are there any significant changes in the structure of both of these metrics of convergence over

time? (d) Is there evidence of spatial dependence in the process of regional income convergence

in the North Carolinian and Virginian Counties?

Our results indicate that the income convergence in the North Carolinian Counties is

more pronounced than those experienced in the Virginian Counties. Evidence of this disparity

was found to a lesser extent in our analysis of β convergence and to a greater extent in σ

convergence. The results from the spatial analysis of regional income convergence carried out in

this paper compliments previous results (i.e. the apparent differences in the two states in terms of

beta and sigma convergence). This study found statistically significant evidence of spatial

dependence occurring in both states at a county level of analysis; however, the spatial lag of



regional income convergence was less significant in our analysis of regional income convergence

in the Virginian Counties than it was in the North Carolinian Counties. The researchers question

whether this inherent heterogeneity has implications for county and state level policy makers in

terms of governance and policy development projects.

The rest of the paper is organized as follows. Section 2 provides a brief review of the

literature, while section 3 discusses the data. Section 4 explains the methodology. This is

followed by the empirical results in section 5 and finally the researchers conclude in section 6.

LITERATURE REVIEW

This paper is interested in examining whether Virginian and North Carolinian Counties

are converging in terms of beta and sigma convergence and if there is evidence of spatial

dependence occurring during this convergence process. From a general perspective, when

researchers evaluate whether a county exhibits beta convergence, according to Barro, Sala-I-

Martin, Blanchard, and Hall (1991), researchers are interested in, “how fast and to what extent

the per capita income of a particular economy is likely to catch up to the average per capita

income across economies” (p. 112-3) and if they want to examine sigma convergence, according

to Barro et al. (1991), researchers need to examine “how the distribution of per capita income

across economies has behaved in the past or is likely to behave in the future” (p. 113). When

researchers examine spatial dependence they are interested in whether certain geographic

associations or distances may offer some explanatory power over how people, according to

Ioannides, Y. and Loury, L. (2004), build information networks, establish neighborhoods, or

create boundaries that either facilitate or impede information sharing based upon their natural

tendency to associate with people that share similar ethnic, occupational, or social ties.

Researchers have paired convergence studies with spatial econometric techniques to

explore the dynamic process of regional income convergence. Rey, S. and Dev, B. (2006) and

Rey, S. and Montouri, B. (1999) analyzed and found statistically significant levels of spatial

dependence and various forms of convergence (i.e. beta and sigma) using a state level of analysis

in the United States. Higgins, Levy, and Young (2006) focused explicitly on exploring growth

and convergence across the U.S., using a county-level of analysis. The aforementioned studies

indicate that spatial relationships influence the convergence process.

Some researchers have explored the process of regional income convergence, whether they focus

on country, state, county, or city levels of analysis, to attempt to gain an understanding of the

generalized process of convergence and the relationship of spatial dependence in this

convergence process. Pede, V., Florax, R., and de Groot, H. (2006) have found that technological

growth is explained by a localized human capital effect as well as a technological catch-up

effect, which influences the convergence process. Rodriguez-Pose, A. and Ezcurra, R. (2010)

relied on a country-level of analysis and questioned whether the centralization of the

redistribution of country level GDP or the degree of localized political power influenced regional

inequalities, which influences regional development and therefore growth. Kerr, W., and

O’Connell (2012) examined whether the degree of industrial agglomeration, in a particular

region, could influence that region’s growth rate. These research findings seem to indicate that

the root causes of regional income convergence, the process driving it, and the spatial

dependence embedded in this process is difficult to model and explain.

The goal of the present study is to determine if there is a disparity in terms of regional beta

convergence, sigma convergence, and spatial dependence between two states that share a similar



geographic proximity. The researcher’s aim is to extend the research of Rey et al. (1999), using a

county level of analysis, and focus on exploring beta and sigma convergence as well as the

significance of the spatial lag of growth on regional income convergence. This paper will

provide a platform from which researchers can analyze the process of regional income

convergence.

DATA

This study used county-level per capita income data for Virginian and North Carolinian

counties. The data was obtained from the U.S. Department of Commerce’s Bureau of Economic

Analysis (BEA). The specific data set is coded as CA1-3 – personal income summary estimates

and the search criteria were 3 Per capita personal incomes. Specifically, for the Virginia data set,

the researchers used both traditional county and independent city data in order to provide a

comprehensive overview of the structure of regional income convergence.

The time horizon and the number of counties used in this study were limited solely by the

data available on the BEA website. According to the BEA there are 71 traditional counties in

Virginia and 34 independent cities / non-traditional counties, which are coded as independent

cities (non-traditional counties), and 100 counties in North Carolina. All traditional and non-

traditional counties had per capita income estimates from 1969 to 2010. In summary, the

combined data set yielded approximately 8,405 unique data points.

In both counties annual data was collected and each individual data point was grouped in

two ways: (a) based upon county affiliation and (b) the year of observation. Grouping the data

this way allowed for the data to be segmented the into cohorts in order explore: (a) Each cohort’s

beta convergence, (b) The correlation amongst the individual counties’ convergence rates with

respect to time, and (c) the sigma convergence between the cohorts over time. Therefore, the

researchers would classify the data obtained to carry out this analysis as panel data.

METHDOLOGY

This study expands the research conducted by Rey and Montouri (1999), in which they

found significant levels of beta and sigma convergence occurring in a state level of analysis. The

researchers build on their study by answering the following hypotheses.

Research Question 1: Using a county-level of analysis, do the counties of Virginia and

North Carolina exhibit regional beta convergence.

Research Question 2: Using a county-level of analysis, do the counties of Virginia and North

Carolina exhibit regional sigma convergence.

Research Question 3: Are there any significant changes in the structure of both of these metrics

of convergence over time?

Research Question 4: Is there evidence of county-level spatial dependence in our Virginian and

North Carolinian Counties?

Research Question 5: If there is significant spatial dependence, can researchers use this

dependence to improve our model of county level growth rate’s predictive power?



The following sections document how the regional beta and sigma convergence was

calculated. Furthermore, the researchers developed an analytical process to expand the results of

the overarching analysis to include more subtle changes in the structural relationships over time.

Beta Convergence

This study applied a basic model to estimate whether a county with a high level of per

capita income at the starting period of the analysis (i.e. 1969) converged, in terms of growth

rates, with counties that exhibited a lower initial starting level. The dependent variable in this

model is the growth rate experienced in county i over time period t, where the starting

observation is time period t and the ending period is time period k. The formulaic representation

of this model is as follows:

(γi,(t+k)−γi,t

γi,t) = α + β ln (γi,t)+ εi,t (1)

γi,(t+k): The per capita income in county i in time period t plus k units of time.

γi,t: The per capita income in county i in time period t.

α: The intercept of the regression equation.

β: The strength and direction of the relationship between the growth rate and the log

of per capita income.

εi,t: The error term for the initial regression

The researchers expect that over a given time horizon (i.e. from 1969 to 2010), the

growth rates (i.e. the dependent variable) for the counties with lower starting per capita incomes

will be higher than the growth rate of counties with higher starting per capita incomes.

In the second component of this initial analysis, the researchers have segmented the data

into yearly cohorts in order to examine whether the relationship between the starting level of per

capita income and growth rates is changing over time. Therefore, this portion of the paper

analyzed whether, in the aggregate, after grouping counties into state cohorts, the correlations

between per capita income and growth rates converge with respect to time. A negative

correlation between these two variables would imply that the states counties were converging

(i.e. the poorer counties were catching up to the richer counties in that year) and a positive

correlation coefficient would imply that the counties in the state were diverging with respect to

time (i.e. the richer counties were getting richer and the poorer counties were becoming poorer).

To summarize, the analysis of beta convergence has attempted to use the results of this

analysis to make some general conclusions about the governing dynamics of the county level

income beta convergence in these two states. In previous studies, researchers have found

statistically significant evidence of beta convergence using country, state, and county levels of

analysis (see Barro, Sala-I-Martin, Blanchard, & Hall, 1991; Rey and Montouri, 1999; Young,

Higgins, & Levy, 2008). However, in this study, the researchers believe that it might be more

useful to evaluate how this dynamic process of convergence changes over time and if there is any

meaningful information hidden in this convergence process.



Sigma Convergence

According to Barrow, Sala-I-Martin, Blanchard, & Hall (1991), if researchers want to

know “how the distribution of per capita income across economies has behaved in the past or is

likely to behave in the future” (p. 113), the relevant metric that researchers should explore is

sigma convergence.

𝜎𝑡 = √1

𝑛∑ (𝑥𝑖,𝑘 − �̅�)2𝑛𝑘=𝑡 (2)

To carry this analysis out, the researchers estimated, first, the standard deviation in

county level per capita income in period t using a cross-section of per capita income in a given

state constrained by the year of analysis. The resulting cross-sectional results were then grouped

by yearly observations and a time series analysis was conducted to determine if, at the county

level of analysis, these two states exhibited significant levels of sigma convergence.

Spatial Dependence

This study will also use the spatially lag model to explain the dependence between our

county of interest and its spatial lag. When researchers use a spatially lagged model, they are

assuming, according to Ward and Gleditsch (2008) that “they believe that the values of y in one

unit i are directly influenced by the values of y found in i’s ‘neighbors’” (p. 35). Researchers can

compare this model with spatial error model, in which, according to Ward et al. (2008),

researchers treat the spatial correlation as a nuisance that should be eliminated—this nuisance

will lead to estimation problems (p. 65). This study assumes that there is information embedded

in ‘neighborhood’ that will have significant explanatory power over what happens in the county

of interest.

EMPIRICAL RESULTS

This section outlines the results of the analysis. The results are segmented into three

broad categories: (a) beta convergence, (b) sigma convergence, and (c) spatial dependence. The

subsections outline the key findings and expand on the interpretation of these findings when

additional analysis seemed necessary. The researchers began by documenting evidence of beta

convergence, moved on to evaluating whether sigma convergence has occurred, turned to

evaluating whether spatial dependence occurred, and finally summarized the research project’s

findings.

Beta Convergence

Beta convergence, or evidence thereof, implies that counties with lower starting per

capita incomes converge towards counties with higher per capita incomes. More succinctly, the

growth rates of poor counties dominate the growth rates of rich counties. The beta convergence

of the counties in the Virginian and North Carolinian counties are illustrated in Figures 1 and

2.Table 1 illustrates the results obtained from the OLS (Ordinary Least Squares) estimation of

the beta convergence obtained in our analysis of Virginian and North Carolinian Counties

segmented into state level cohorts from 1969 to 2010.



In both states, at a county-level of analysis, the researchers have identified statistically

significant county-level beta convergence. The estimates of regional income convergence are

significant using an α of less than .01. Therefore, the reader can be over 99% sure that the

counties studied in this paper are exhibiting statistically significant evidence of β convergence.

The Virginian Counties have an interesting structure because they are broken up into two

distinct groups: (a) Traditional Counties and (b) Independent Cities. Table 1 illustrates that the

Virginian Counties exhibited statistically significant evidence of β convergence over time. To

enhance the analysis of the Virginian Counties, the researchers segmented the two distinct

cohorts defined in this analysis based upon their affiliation with either: (a) the ‘traditional

county’ or (b) the ‘independent county’ cohort. Table 2 provides the results of three OLS

regression analyses that illustrate the differences between the traditional counties and

independent cities. The first regression calculates the β convergence amongst traditional

counties—the results of this analysis were similar to those reported on the full sample of Table 1,

primarily because the traditional counties dominated the sample, in terms of observations. The

next regression presented in Table 2 illustrates how the β convergence deteriorates as the reader

looks solely at the independent cities in the analysis; overall, using a county level of analysis,

there is statistically significant evidence of regional income convergence.

Similar to Barro, Sala-I-Martin, Blanchard, & Hall (1991), Rey & Montouri (1999), and

Young, Higgins, & Levy (2008), this research project finds evidence of beta convergence. To

expand this research project, the researchers decided to evaluate whether the structure of the

relationship between the starting level of per capita income and growth is changing over time.

This analysis was executed by examining the yearly cross-sectional correlation between starting

level per capita income and growth rates from 1969 to 2010. Figure 3 displays the results of the

correlation analysis on North Carolinian Counties. By reviewing Figure 3 and Table 3 together

the reader can see that over time, there does not seem to be a time-trend between the

convergence statistics over time in the North Carolinian Counties.

In the initial examination of the changes in the structure of the convergence statistics in

the Virginian Counties, see Table 3 – Virginian Counties (1969 to 2010), there appeared to be

evidence of a slight structural shift in the convergence statistics (i.e. evidence of a shift of beta

convergence to beta divergence).The relationship between starting per capita income and growth

is trending towards divergence over time—evidence of this is the positive slope in the plot of

correlation over time. The third analysis presented in Table 3 (i.e. Virginian Counties 1969 to

2005) illustrates that if the researchers were to limit our regression analysis to the 1969 to 2005

time period, they would find that the structural changes in correlation between starting per capita

income and growth rates is changing over time and that change has been economically and

statistically significant.

The data presented in Table 1 and Figures 1 through 4 indicate that from 1969 to 2010

the counties within Virginia and North Carolina exhibited statistically significant β convergence.

A more comprehensive analysis of the underlying processes driving this β convergence seems to

provide another interesting story. The data presented in Tables 2 and 3 and Figures 3 and 4 seem

to indicate that the structure of β convergence experienced in North Carolinian and Virginian

Counties are dissimilar. There is no hard evidence of structural changes in the rates of β

convergence occurring in this study; however, it seems clear that in Virginia a gradual shift in β

convergence has been occurring from 1969 to 2010. It is the researchers’ belief that a thorough



analysis of β convergence would include an analysis of the more subtle changes in the

convergence process over time.

Sigma Convergence

This section evaluated whether the counties in the state cohorts exhibited signs of σ

convergence (i.e. Sigma Convergence). When researchers explore σ convergence over time they

are expecting to find that the dispersion between the individual counties per capita income is

declining over time. Figure 5 and Table 4 illustrate that the deviation in per capita income,

approximated by the standard deviation in per capita income at time t, is decreasing over time.

This finding supports the expectation that the dispersion of per capita incomes are decreasing

over time; however, when the researchers examined the dispersion of per capita income over

time in Virginian Counties, they found a different trend or evidence that the dispersion between

Virginian Counties per capita income was increasing over time and that this divergence was

significant (See Table 4 and Figure 6).

Given that the two states experienced significant differences in both (a) the general

direction of σ convergence and (b) the magnitude of sigma convergence, the researchers believed

that it might be useful to explore whether the magnitude and tendency of sigma divergence

experienced in the Virginian Counties could be due to the structure of the Virginian Counties

analyzed in this study. Table 4, line items 3 and 4, document the relative rates of σ divergence

experienced in traditional and independent cities in Virginian Counties. Divergence is more

pronounced in independent cities when compared against traditional counties. However, when

the traditional and nontraditional counties are grouped together, the statistical significance

attached σ divergence deteriorates. The results of this analysis indicate that the dispersion of per

capita income in the Virginian counties is increasing and the increase is both economically and

statistically significant.

Spatial Dependence

This section of the analysis determines whether there was statistically significant

evidence of spatial dependence in our county-level analysis of the two states regional income

convergence and if the spatial dependence of growth rates can be used to improve the model of

regional income convergence’s predictive power. Initially, the researchers were interested in

whether the two states, using a county level of analysis, exhibited county level spatial

dependence. Table 5 presents the result of the analysis of spatial dependence using a county level

analysis. Both states generated statistically significant results in terms of spatial dependence, but

the evidence of spatial dependence was more pronounced in North Carolinian Counties. Using

the results of this analysis, the researchers evaluated whether the spatial component added any

predictive power to our models of regional income convergence.

Table 6 presents the results of our regional income convergence models including the

spatial lag of growth rates. After running multivariate regression analyses including the spatial

lag of regional income convergence for Virginian and North Carolinian Counties the results for

the two states are, again, dissimilar. The final model of regional income convergence for North

Carolinian Counties included a spatial lag, whereas the model for Virginian Counties does not

include a spatial component and is equivalent to Formula 1.

(γi,(t+k)−γi,t

γi,t) = α + β ln (γi,t)+ ρWyi + εi,t (2)



γi,(t+k): The per capita income in county i in time period t plus k units of time.

γi,t: The per capita income in county i in time period t.

ρWyi: The spatial lag of growth rates based upon boundary sharing

α: The intercept of the regression equation.

β: The strength and direction of the relationship between the growth rate and the log

of per capita income.

εi,t: The error term for the initial regression

Table 6 presents the restricted and unrestricted models of regional income convergence

for both the Virginian and North Carolinian Counties—the spatial lag of growth rates was the

variable of interest. Next, an f test was conducted to determine if beta coefficient attached to the

spatial lag of growth rates was significantly different from zero when the spatial component was

included in the multivariate regression analysis of regional income convergence. Again, the

process of convergence between the two states is dissimilar: (a) For the North Carolinian

Counties, the researchers found statistically significant evidence that the spatial lag of growth

adds predictive power to our model and (b) For the Virginian Counties, the researchers could not

conclude that the spatial lag of growth added predictive power to our model; therefore, the

spatial component was dropped from the final model for Virginia.

CONCLUSION

The goals in this study were to answer five research questions, using a county level of

analysis: (a) Do the counties of Virginia and North Carolina exhibit β convergence, (b) Do the

counties of Virginia and North Carolina exhibit σ convergence, (c) Are there any structural

changes experienced in North Carolinian and Virginian Counties over time, (d) Is there evidence

of spatial dependence in the county level growth rates in Virginia and North Carolina, and (e)

Does the addition of the spatial lag of growth rates improve the models of regional income

convergence in our two states? This paper provides the answers to these research questions using

data obtained from the Bureau of Labor Statistic from 1969 to 2010. In the following paragraphs

the researchers will provide a summary of the research results obtained as a result of exploring

each of the research questions.

In the first section of this analysis the researchers analyzed whether Virginian and North

Carolinian counties exhibited evidence of β convergence. The results of this analysis support the

expectation—both states exhibit statistically and economically significant evidence of β

convergence; however, in terms of economic significance the β convergence experienced in the

North Carolinian counties was more significant. Due to the unique county structure found in

Virginia Counties, the researchers believed that it would be useful to examine the difference in

the rates of β convergence experienced in traditional and independent city counties. The

researchers found that the difference between the two cohort’s β convergences was significant;

however, the dissimilarities between the independent and traditional county’s β convergence had

a minimal effect on the results of our analysis of β convergence in the Virginia Counties because

the traditional counties dominated our independent cities in terms of observational units.

To provide a more comprehensive analysis of β convergence the researchers thought that it

would be worthwhile to segment the convergence statistics by year and evaluate how the cross-

sectional statistics change over time. In North Carolina the cross-sectional β convergence



coefficients did not display economically or statistically significant variation over time; however,

in our analysis of Virginian Counties, the variation of cross-sectional β convergence did change

over time and if the model is constrained to the following time horizon, from 1969 to 2005, the

change in the Virginian Counties was economically and statistically significant. The researchers

provided evidence that seems to suggest that the Virginian Counties are experiencing an

economically and statistically significant shift in β convergence over time or, more succinctly,

that the convergence rates experienced between the rich and the poor counties seem to be

trending towards divergence over time.

The analysis of σ convergence of North Carolinian and Virginian Counties supports the

findings previously documented in this analysis. The per capita income in North Carolinian

Counties identified in this analysis seem to be converging over time or the dispersion of per

capita incomes seem to be decreasing over time in the North Carolinian cohort. The results of the

findings of Virginian County’s σ convergence seem to, again, diverge from theoretical

expectations. The Virginian Counties seem to be exhibiting economically and statistically

significant divergence in terms of σ convergence. The structural relationship of the Virginian

Counties does not seem to create this divergence, because if the individual county-level σ

convergence is evaluated grouped based upon traditional and independent city cohorts, the

researchers find that the significance levels of σ divergence increases over time.

The analysis of spatial dependence occurring at a county level of analysis in these two

states, again finds a divergence in terms of results. This study finds statistically significant

evidence of spatial dependence of growth rates in both Virginian and North Carolinian Counties.

However, when the researchers questioned whether the spatial component of growth rates should

be included in the final model of regional income convergence in the North Carolinian and

Virginian Counties, the researchers found statistically significant evidence that the coefficient for

the spatial lag of growth was significantly different from zero. In terms of the Virginian

Counties, the researchers could not conclude that the addition of the spatial lag of growth added

enough predictive power to our model to include; therefore, the spatial lag of growths rates was

removed from the final model of growth for the Virginian Counties.

The researchers believe that the results of this study motivate a prescriptive study from a

policy setting standpoint using states like Virginia and North Carolina that share a geographic

boundary, whose beta and sigma convergence, as well as spatial dependence, are dissimilar.

Future research should provide some clues in regards to why this divergence is occurring,

potential public policy prescriptions that could be implemented to change this divergence, and

hint at structural changes to governance that might either speed up or slow down the potential

rate of convergence using a county level of analysis. For example, researchers could use the

results found in Rodriguez-Pose, A. and Ezcurra, R. (2010) and question whether these two

states differ in terms of the degree of (de)centralization of their redistribution of state level GDP

or whether the political bargaining capacity of the various counties within these two states are

significantly different. From another perspective, researchers could take the work of Ghani, E.,

Kerr, W., and O’Connell (2012) and examine whether the industrial structure of a county may

cause localized agglomeration of counties within the state that may in turn influence the structure

of the work force and entrepreneurial activity within these counties, which have been shown to

effect regional growth rates (see Fritsch, M., 2008).



REFERENCES

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TABLES & FIGURES

Figures 1 & 2: Regional Income Convergence in Virginian and North Carolinian Counties

Table 1: Comparison of Virginian and North Carolinian Regional Income Convergence

Comparison of Virginian and North Carolinian Regional Income Convergence

�̂� Standard Error R-Squared

Virginian -0.072 0.009 0.379

p value (.000) North Carolinian -0.100 0.008 0.612

p value (.000) Notes: B-Hat is the estimated regional income convergence statistic estimated based upon the

convergence experienced in the Virginian and North Carolinian Counties from 1969 through 2010.

Table 2: Virginian Counties (Traditional & Independent City)

Virginian Counties (Traditional & Independent City)


Traditional Counties -0.075 0.012 .352

p value (.000) Independent Cities -0.042 0.016 .187

p value (.011) Notes: B-Hat is the estimated regional income convergence statistic estimated based

upon the convergence experienced in the Virginian Counties from 1969 through 2010.

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-4 -2 0 2 4

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Standardized Growth Rates

Beta Convergence (Virginian Counties)

-2.5

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Standardized Growth Rates

Beta Covergence (North Carolinian Counties)



Figures 3 & 4: Correlation Analysis of North Carolinian and Virginian Counties – β

Convergence

Notes: The correlation between Growth and Per Capita Income was calculated using the following

formula 𝐸[(𝑋𝑖−𝜇𝑥)(𝑌𝑖−𝜇𝑌)

𝜎𝑥𝜎𝑌. The yearly cross-sectional correlation coefficients were plotted on the Y axis

and the year of observation was plotted on the X axis.

Table 3: Virginian Counties (Traditional & Independent City)

Virginian Counties (Traditional & Independent City)

�̂� Standard Error R Squared

North Carolinian Counties 0.002 0.003 0.014

p value (.464) Virginian Counties (1969 to 2010) 0.004 0.003 0.059

p value (.124) Virginian Counties (1969 to 2005) 0.009 0.002 0.252

p value (.001) Notes: B-Hat is the beta coefficient that describes the evolution of the relationship

between the correlation of starting per capita income and growth rates over time.

-0.8

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0

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0.4

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North Carolinian Counties Correlation Between Starting Per Captia Income and Growth

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Virginian Counties Correlation Between Starting Per Captia Income and Growth



Figures 5 & 6: Regional σ Convergence in North Carolinian and Virginian Counties from 1969

to 2010.

Notes: σ convergence identified in time t using a cross-section of log per capita income was calculated

using the following formula: 𝜎𝑡 = √1

𝑛∑ (𝑥𝑖,𝑘 − �̅�)2𝑛𝑘=𝑡

Table 4: σ Convergence

σ Convergence


North Carolina -0.00035 0.00012 .17623

p value (.00565) Virginia (Traditional / Independent Cities) .00110 .00010 .68800

p value (.00010) Virginia (Traditional Counties) .00120 .00010 .71620

p value (.00000) Virginia (Independent Cities) .00150 .00010 .85270

p value (.00000) Notes: B-Hat is the estimated regional income sigma convergence statistic estimated based

upon the convergence experienced in the Virginian and North Carolinian Counties from 1969 through 2010.

0.12

0.14

0.16

0.18

0.21

96

9

19

73

19

77

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σ Convergence - North Carolina

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0.26

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σ Convergence - Virginia



Table 5: County Level Spatial Dependence (Virginia and North Carolina)

Spatial Regression Results

Statistics Virginia North Carolina

Intercept 0.0000 0.0000

St Error 0.0929 0.0857

p value 0.0008 0.0000

Beta -0.3210 -0.5220

St Error 0.0933 0.0862

p value 0.0008 0.0000

R2 0.1031 0.2725

p value 0.0008 0.0000

Table 6: Regression Analysis of Virginian and North Carolinian Counties

Statistics NC (Unrestricted) NC (Restricted) VA (Unrestricted) VA (Restricted)

Intercept 0.8514 1.1039 0.8004 0.8927

St Error 0.0893 0.0636 0.1025 0.0725

p value 0.0000 0.0000 0.0000 0.0000

Beta (Per Capita Income) -0.0828 -0.1004 -0.0685 -0.0724

St Error 0.0089 0.0081 0.0096 0.0091

p value 0.0000 0.0000 0.0000 0.0000

Beta (Spatial Lag) 0.3633

0.1930 St Error 0.0956

0.1518

p value 0.0003

0.0000

R2 0.6619 0.6115 0.3892 0.3735

p value 0.0000 0.0000 0.0000 0.0000

F test - p value 0.0003

0.2063

spatial econometric analysis of regional income convergence ...analysis (bea). the specific data set...

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